More recently, many enlightening ideas from other fields, such as condensed matter physics, quantum information theory, network flow optimization theory, etc., have entered and benefited the study of the holographic gravity. One of the most striking examples is that inspired by the tensor network method originally used in condensed matter physics as a numerical simulation tool to investigate the wave functions of quantum many-body systems, various holographic tensor network (TN) models have been constructed as toy models of the holographic duality, such as MERA (multiscale entanglement renormalization ansatz) tensor network [1]}, [2]}, [3]}, [4]}, perfect tensor network [5]}, random tensor network [6]}, p-adic tensor network [7]}, [8]}, [9]}, OSED (one-shot entanglement distillation) tensor network [10]}, [11]}, [12]} and so on. For more research on tensor networks in the holographic context, see e.g. [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}. Furthermore, inspired by the continuous version of the holographic tensor network models, especially the construction of cMERA (continuous MERA) tensor network [30]},  [31]}, [32]} proposed the so-called SS correspondence (surface/state correspondence) as a more specific mechanism of the holographic principle. The SS duality refers to the duality between a codimension two convex surface \(\Sigma \)  in the holographic bulk spacetime and a quantum state described by a density matrix \(\rho (\Sigma )\) , which is defined on the Hilbert space of the quantum theory dual to the Einstein's gravity. This can be understood intuitively in the context of tensor networks. For a convex closed surface \(\Sigma \) , we can always contract the indices of tensors contained in the region enveloped by \(\Sigma \)  to obtain a state \(\rho (\Sigma )\) .
